# Questions tagged [geometry]

This challenge is intended to be solved by using, manipulating, or creating shapes or other geometric structures.

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### Counting symmetric grid chains

Notation and definitions Let $[n] = \{1, 2, ..., n\}$ denote the set of the first $n$ positive integers. A polygonal chain is a collection of connected line segments. The corner set of a ...
32 views

### Area of diagonal-folded regular polygon

I have a piece of paper whose shape is a regular n-gon with side length 1. Then I fold it through some of its diagonals. What is ...
2k views

### Does this line pass through that square?

Divide the first quadrant (including the positive x-axis, the positive y-axis, and the origin) into 1x1 grids, with each grid labelled by the coordinates of its bottom-left corner, as demonstrated ...
1k views

### Is it rectilinear?

Today's challenge: Given an ordered list of at least 3 unique integer 2D points forming a polygon, determine if the resulting polygon is Rectilinear. A polygon is rectilinear if every interior ...
4k views

### Billiard balls collision

Given the 2-dimensional positions and velocities of a pair of billiard balls right before impact, calculate their velocities after a perfectly elastic collision. The balls are assumed to be ideal ...
547 views

### Counting generalized polyominoes

This challenge will have you count pseudo-polyforms on the snub square tiling. I think that this sequence does not yet exist on the OEIS, so this challenge exists to compute as many terms as possible ...
810 views

In mathematics, a cyclic quadrilateral is one whose vertices all lie on the same circle. In other words, every vertex is on the circumcircle of the other three. For more information, see the MathWorld ...
1k views

### Triangular Manhattan Distance

The Manhattan distance on a regular grid is the number of orthogonal steps one needs to take to reach one cell from another. Orthogonal steps are those that go through the edges of the grid cells (as ...
131 views

### Rotated analog clock [closed]

Given: a 12 hour time t in hours and minutes, a rotation r in degrees, return the time shown when an analog clock that is ...
1k views

### Write a function that returns an iterable object of all valid points 4-directionally adjacent to (x, y)

A very common need in algorithms classes and computer science in general is to iterate 4-directionally over a grid or matrix (such as in BFS or DFS). This seems to often result in a lot of clunky and ...
6k views

### Random point on a sphere

The Challenge Write a program or function that takes no input and outputs a vector of length $1$ in a theoretically uniform random direction. This is equivalent to a random point on the sphere ...
23k views

### Draw the national flag of Iceland

This year's UEFA Euro 2016 is over and besides a couple of negative headlines there has been a very positive surprise as well – the Iceland national football team. Let's draw their national flag. ...
4k views

### Count the number of triangles

Given a list of positive integers, find the number of triangles we can form such that their side lengths are represented by three distinct entries of the input list. (Inspiration comes from CR.) ...
2k views

### Do these squares overlap?

Given the coordinates of the upper left corners of two squares and their side lengths, determine whether the squares overlap. A square includes the top and left lines, but not the bottom and right ...
7k views

### Angle between the hands on a clock [duplicate]

Given the time in 24 hour format (2359 = 11:59pm) return the angle between the minute and hour hands on a standard clock (on the ...
375 views

### ​Plane​ ​Blow​up​

The Blow-up is a powerful tool in algebraic geometry. It allows the removal of singularities from algebraic sets while preserving the rest of their structure. If you're not familiar with any of that ...
2k views

### Triangular Lattice Points close to the Origin

Background A triangular grid is a grid formed by tiling the plane regularly with equilateral triangles of side length 1. The picture below is an example of a triangular grid. A triangular lattice ...
565 views

### The Knight's estate

And then the King said: You fought bravely, Knight, and your deed will not be forgotten for centuries. For your valor I grant you this castle and the lands around it. Things rush me, and I can not ...
1k views

### Circle intersection area

Description : Given x and y positions of two circles along with their radii, output the ...
3k views

### Construct a pentagon avoiding compass use

Rules You will start with only two elements: Points $A$ and $B$ such that $A \neq B$. These points occupy a plane that is infinite in all directions. At any step in the process you may do any ...
1k views

### Count the squares

Challenge Origami (folding paper) is a creative form of art. As far as I know, master of Origami prefers square paper. Let's start from beginning - convert a rectangular paper to a square one. So ...
821 views

### Expand a hexagon

Given an ASCII art hexagon as input, output one whose sides are all one unit longer. ...
7k views

### Golf the smallest circle!

The problem: Given a non-empty set of points in the Cartesian plane, find the smallest circle that encloses them all (Wikipedia link). This problem is trivial if the number of points is three or ...
4k views

### Evaluate the aspect ratio of a triangle

Given three sidelengths of a triangle, evaluate its aspect ratio AR given the following formula: where The closer to equilaterality a triangle is, the closer to 1 ...
1k views

### Area of a 2D convex hull

You are given an array/list/vector of pairs of integers representing cartesian coordinates $(x, y)$ of points on a 2D Euclidean plane; all coordinates are between $−10^4$ and $10^4$, duplicates ...
272 views

### Partition and Restructure

Given two contiguous shapes of the same area, determine the optimal way to divide the first shape into a minimum number of contiguous segments such that they can be rearranged to form the second shape....
12k views

### Draw the South Korean flag

When I stumbled upon this question I remembered that I had also once seen precise rules for the construction of the South Korean flag. And this is quite a different construction. Source: Wikipedia ...
632 views

### Dihedral group D4 composition with custom labels

The dihedral group $D_4$ is the symmetry group of the square, that is the moves that transform a square to itself via rotations and reflections. It consists of 8 elements: rotations by 0, 90, 180, ...
3k views

### What is the area of this polygon?

Calculate the area of a polygon. Inspired by this shoelace algorithm video. Task Your job is to create a program or function that calculates the area of a polygon. Program or function is defined ...
31k views

### Draw an Image as a Voronoi Map

Credits to Calvin's Hobbies for nudging my challenge idea in the right direction. Consider a set of points in the plane, which we will call sites, and associate a colour with each site. Now you can ...
10k views

### Little Chandler is sad. Draw him a cloud to cheer him up

Little Chandler is sad. Draw him a cloud to cheer him up. Note: Drawing a cloud won't actually cheer him up. A circle can be defined as a 3-tuple (x,y,r) where <...
368 views

### Rectangular difference

In this challenge, you are given two overlapping rectangles, and you need to calculate the rectangles created by removing one from the other. For example, if you remove the red rectangle from the ...
4k views

### Diamond creator +

Challenge : Given an integer n as input. Create a diamond that is 2x the given number n. Input : Input is integer ...
272 views

### Stereographic projection of polyhedra

You will create a program that generates the stereographic projection of polyhedra. In particular, to keep things simple, we'll only focus on n-chamfered dodecahedron. Given a natural number ...
604 views

### How lit is this room? 🔥 pt. 1

Related to this question. A room is defined to be a (not necessarily convex) non-intersecting polygon, expressed as an ordered list of 2-dimensional coordinates. A sufficiently bright lightbulb is ...
343 views

### Can this container hold this much liquid?

Can this container hold this much liquid? Challenge Synopsis As you most likely know, liquids have an indefinite shape and a definite volume. As such, they always take the shape of their container. ...
8k views

### Check if point lies inside triangle

Your goal is to determine whether a given 2D point X lies within the area of the triangle with given vertices A,B,C. Write a function that takes in the coordinates of the test point X and the three ...
5k views

### Covering a Skyline with brush strokes

Given a non-negative integer skyline height list, answer how many uninterrupted 1-unit-high horizontal brush strokes are needed to cover it. [1,3,2,1,2,1,5,3,3,4,2]...
1k views

### Code-Golf: Lattice Points inside a Circle

The following picture shows the problem: Write a function that, given an integer as the circle radius, calculates the number of lattice points inside the centered circle (including the boundary). ...
7k views

### Let's draw the flag of Nepal

Nepal’s flag (Wikipedia, Numberphile) looks very different from any other. It also has specific drawing instructions (included in the Wikipedia article). I want you guys to make a program which will ...
9k views

### Is my triangle right?

Given a, b, c the length of the three sides of a triangle, say if the triangle is right-angled (i.e. has one angle equal to 90 degrees) or not. Input Three ...
850 views

### A cube of text ݀

Last time you made a square of text, but now, can you make a cube of text? The Challenge Given a string, output the string in the form of a cube. You can assume the string will always have 2 chars ...
2k views

### Create a grid as close to a square as possible

Create a function or program that makes a grid as close to an square as possible You will be given an integer N as input, whole numbers (1,2,3,25, etc) The output must be a perfect rectangular grid ...
2k views

### Distance between two points on the Moon

Given latitude/longitude of two points on the Moon (lat1, lon1) and (lat2, lon2), compute the distance between the two points in ...
285 views

### Count the Closed Polygons

Input: An NxM grid or multi-line string (or other reasonable input-format), containing only printable ASCII (unicode range ...
405 views

### Hilbertize an image

For a computer vision app I want to do a mapping of an image, in such a way that every pixel fit hilbert curve, instead of conventional layout. So task could be as follows: Task description Given ...
4k views

### Visually Explain the Pythagorean Theorem

A common visual explanation of the Pythagorean theorem is as such: The squares are meant to represent the side length's squared, and the areas of a + b = c, just ...
1k views

### The World in the Future [closed]

In the future, the world will change, there's no doubt about it. For that reason, you have to produce a realistic map of the world n years in the future. The ...